THE BEHAVIOR OF FORECAST ERRORS FROM A NEARLY INTEGRATED AR(1) MODEL AS BOTH SAMPLE SIZE AND FORECAST HORIZON BECOME LARGE
研究了当真实过程接近单位根且样本量和预测期同步增大时，估计的AR(1)模型预测误差的渐近分布，发现其由两个渐近独立的分量组成，其中一个是非正态的，因此正态近似不适用。
We develop asymptotic approximations to the distribution of forecast errors from an estimated AR(1) model with no drift when the true process is nearly I (1) and both the forecast horizon and the sample size are allowed to increase at the same rate. We find that the forecast errors are the sums of two components that are asymptotically independent. The first is asymptotically normal whereas the second is asymptotically nonnormal. This throws doubt on the suitability of a normal approximation to the forecast error distribution. We then perform a Monte Carlo study to quantify further the effects on the forecast errors of sampling variability in the parameter estimates as we allow both forecast horizon and sample size to increase.